Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.8% → 98.3%

Time: 4.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x_m \cdot \left(y + z\right)}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq 5 \cdot 10^{+75} \lor \neg \left(t_0 \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;\frac{x_m}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (* x_m (+ y z)) z)))
   (*
    x_s
    (if (or (<= t_0 5e+75) (not (<= t_0 5e+303))) (/ x_m (/ z (+ y z))) t_0))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = (x_m * (y + z)) / z;
	double tmp;
	if ((t_0 <= 5e+75) || !(t_0 <= 5e+303)) {
		tmp = x_m / (z / (y + z));
	} else {
		tmp = t_0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x_m * (y + z)) / z
    if ((t_0 <= 5d+75) .or. (.not. (t_0 <= 5d+303))) then
        tmp = x_m / (z / (y + z))
    else
        tmp = t_0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = (x_m * (y + z)) / z;
	double tmp;
	if ((t_0 <= 5e+75) || !(t_0 <= 5e+303)) {
		tmp = x_m / (z / (y + z));
	} else {
		tmp = t_0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = (x_m * (y + z)) / z
	tmp = 0
	if (t_0 <= 5e+75) or not (t_0 <= 5e+303):
		tmp = x_m / (z / (y + z))
	else:
		tmp = t_0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(Float64(x_m * Float64(y + z)) / z)
	tmp = 0.0
	if ((t_0 <= 5e+75) || !(t_0 <= 5e+303))
		tmp = Float64(x_m / Float64(z / Float64(y + z)));
	else
		tmp = t_0;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = (x_m * (y + z)) / z;
	tmp = 0.0;
	if ((t_0 <= 5e+75) || ~((t_0 <= 5e+303)))
		tmp = x_m / (z / (y + z));
	else
		tmp = t_0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(N[(x$95$m * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[Or[LessEqual[t$95$0, 5e+75], N[Not[LessEqual[t$95$0, 5e+303]], $MachinePrecision]], N[(x$95$m / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 5.0000000000000002e75 or 4.9999999999999997e303 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 84.5%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 83.8%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 83.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. associate-/r/ 97.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

   6. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

   if 5.0000000000000002e75 < (/.f64 (*.f64 x (+.f64 y z)) z) < 4.9999999999999997e303

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+75} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -5.8e+94) x_m (if (<= z 2.6e+146) (* (+ y z) (/ x_m z)) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -5.8e+94) {
		tmp = x_m;
	} else if (z <= 2.6e+146) {
		tmp = (y + z) * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.8d+94)) then
        tmp = x_m
    else if (z <= 2.6d+146) then
        tmp = (y + z) * (x_m / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -5.8e+94) {
		tmp = x_m;
	} else if (z <= 2.6e+146) {
		tmp = (y + z) * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -5.8e+94:
		tmp = x_m
	elif z <= 2.6e+146:
		tmp = (y + z) * (x_m / z)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -5.8e+94)
		tmp = x_m;
	elseif (z <= 2.6e+146)
		tmp = Float64(Float64(y + z) * Float64(x_m / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -5.8e+94)
		tmp = x_m;
	elseif (z <= 2.6e+146)
		tmp = (y + z) * (x_m / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -5.8e+94], x$95$m, If[LessEqual[z, 2.6e+146], N[(N[(y + z), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e94 or 2.60000000000000014e146 < z

   1. Initial program 69.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 65.1%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 65.1%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 88.3%

      \[\leadsto \color{blue}{x} \]

   if -5.7999999999999997e94 < z < 2.60000000000000014e146

   1. Initial program 93.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 91.8%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-56} \lor \neg \left(y \leq 2.3 \cdot 10^{+58}\right):\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= y -3.3e-56) (not (<= y 2.3e+58))) (* x_m (/ y z)) x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -3.3e-56) || !(y <= 2.3e+58)) {
		tmp = x_m * (y / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.3d-56)) .or. (.not. (y <= 2.3d+58))) then
        tmp = x_m * (y / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -3.3e-56) || !(y <= 2.3e+58)) {
		tmp = x_m * (y / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -3.3e-56) or not (y <= 2.3e+58):
		tmp = x_m * (y / z)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -3.3e-56) || !(y <= 2.3e+58))
		tmp = Float64(x_m * Float64(y / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -3.3e-56) || ~((y <= 2.3e+58)))
		tmp = x_m * (y / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -3.3e-56], N[Not[LessEqual[y, 2.3e+58]], $MachinePrecision]], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999984e-56 or 2.30000000000000002e58 < y

   1. Initial program 94.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 88.3%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 72.3%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   7. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -3.29999999999999984e-56 < y < 2.30000000000000002e58

   1. Initial program 79.5%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 80.5%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-56} \lor \neg \left(y \leq 2.3 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-58} \lor \neg \left(y \leq 145000000000\right):\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -2.5e-58) (not (<= y 145000000000.0))) (* y (/ x_m z)) x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -2.5e-58) || !(y <= 145000000000.0)) {
		tmp = y * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.5d-58)) .or. (.not. (y <= 145000000000.0d0))) then
        tmp = y * (x_m / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -2.5e-58) || !(y <= 145000000000.0)) {
		tmp = y * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -2.5e-58) or not (y <= 145000000000.0):
		tmp = y * (x_m / z)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -2.5e-58) || !(y <= 145000000000.0))
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -2.5e-58) || ~((y <= 145000000000.0)))
		tmp = y * (x_m / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -2.5e-58], N[Not[LessEqual[y, 145000000000.0]], $MachinePrecision]], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999989e-58 or 1.45e11 < y

   1. Initial program 94.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 76.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   7. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   if -2.49999999999999989e-58 < y < 1.45e11

   1. Initial program 78.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 81.7%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-58} \lor \neg \left(y \leq 145000000000\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-60} \lor \neg \left(y \leq 145000000000\right):\\ \;\;\;\;\frac{x_m \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1.02e-60) (not (<= y 145000000000.0))) (/ (* x_m y) z) x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.02e-60) || !(y <= 145000000000.0)) {
		tmp = (x_m * y) / z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.02d-60)) .or. (.not. (y <= 145000000000.0d0))) then
        tmp = (x_m * y) / z
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.02e-60) || !(y <= 145000000000.0)) {
		tmp = (x_m * y) / z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -1.02e-60) or not (y <= 145000000000.0):
		tmp = (x_m * y) / z
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -1.02e-60) || !(y <= 145000000000.0))
		tmp = Float64(Float64(x_m * y) / z);
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -1.02e-60) || ~((y <= 145000000000.0)))
		tmp = (x_m * y) / z;
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -1.02e-60], N[Not[LessEqual[y, 145000000000.0]], $MachinePrecision]], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999994e-60 or 1.45e11 < y

   1. Initial program 94.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]

   if -1.01999999999999994e-60 < y < 1.45e11

   1. Initial program 78.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

      2. *-commutative 81.7%

         \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-60} \lor \neg \left(y \leq 145000000000\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \frac{x_m}{\frac{z}{y + z}} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (/ x_m (/ z (+ y z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m / (z / (y + z)));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * (x_m / (z / (y + z)))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m / (z / (y + z)));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * (x_m / (z / (y + z)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(x_m / Float64(z / Float64(y + z))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * (x_m / (z / (y + z)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(x$95$m / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 84.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

   2. *-commutative 84.2%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

3. Simplified 84.2%

   \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative 84.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

   2. associate-/r/ 95.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

6. Applied egg-rr 95.0%

   \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

7. Final simplification 95.0%

   \[\leadsto \frac{x}{\frac{z}{y + z}} \]
8. Add Preprocessing

Alternative 7: 52.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot x_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 84.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

   2. *-commutative 84.2%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]

3. Simplified 84.2%

   \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 51.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 51.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))

C

double code(double x, double y, double z) {
	return x / (z / (y + z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (z / (y + z))
end function

Java

public static double code(double x, double y, double z) {
	return x / (z / (y + z));
}

Python

def code(x, y, z):
	return x / (z / (y + z))

Julia

function code(x, y, z)
	return Float64(x / Float64(z / Float64(y + z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x / (z / (y + z));
end

Wolfram

code[x_, y_, z_] := N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))